Physics Spring 2012 Chapter 6 - Momentum Momentum Impulse Impulse Changes Momentum Bouncing Conservation of Momentum Collisions More Complicated Collisions

Physics Spring 2012 Momentum Massive objects are harder to stop! (supertanker cuts engines 25 km from port) Momentum is mass times velocity Momentum = mass * velocity Momentum is conserved in a closed system with no external forces Momentum (initial) = Momentum (final)

Physics Spring 2012 Momentum and Impulse Impulse (J) = Force * Time Interval Impulses change momentum (p) F x t = (ma)t = m x (at) = m x  v Impulse = F x t =  (mv)

Physics Spring 2012 Momentum and Impulse Large change in momentum in a large time

Physics Spring 2012 Momentum Large change in momentum in a small time

Physics Spring 2012 Momentum

Physics Spring 2012 Class Problem If a Mack truck and a Volkswagen have a head-on collision, which vehicle will experience the greater impact force? A) the Mack truck B) the Volkswagen C) both the same D)... it depends on other factors

Physics Spring 2012 Class Problem The answer is c: Both will experience the same impact force, in accord with Newton's 3rd Law. The force that body A exerts on body B is equal and opposite to the force that body B exerts on body A. The effects of these forces, however, are quite different—note from Newton's 2nd Law F truck /M truck = a truck F car /m car = a car So the car decelerates much more than the massive truck.

Physics Spring 2012 Class Problem Which would be more damaging; driving into a massive concrete wall, or driving at the same speed into a head-on collision with an identical car traveling toward you at the same speed? A)Wall B)Head-on Collision C)Same

Physics Spring 2012 Class Problem answer Both cases are equivalent, because either way, your car rapidly decelerates to a dead stop. The dead stop is easy to see when hitting the wall, and a little thought will show the same is true when hitting the car. If the oncoming car were traveling slower, with less momentum, you'd keep going after collision with more "give," and less damage (to you!). But if the oncoming car had more momentum than you, it would keep going and you'd snap into a sudden reverse with greater damage. Identical cars at equal speeds means equal momenta—zero before, zero after collision.

Physics Spring 2012 Conservation of Momentum

Physics Spring 2012 Collisions Two types of collisions –Elastic: Energy not dissipated out of kinetic energy Bouncy –Inelastic: Some energy dissipated to other forms Sticky Perfect elasticity unattainable (perpetual motion)

Physics Spring 2012 Elastic Collision: Billiard Balls Whack stationary ball with identical ball moving at velocity v cue 8 To conserve both energy and momentum, cue ball stops dead, and 8-ball takes off with v cue Momentum conservation: mv cue = mv cue, after + mv 8-ball 8 Since cue ball can’t move through 8-ball, cue ball gets stopped.

Physics Spring 2012 Real-World Collisions Is a superball elastic or inelastic? –It bounces, so it’s not completely inelastic –It doesn’t return to original height after bounce, so some energy must be lost Superball often bounces 80% original height –Golf ball  65% –Tennis ball  55% –Baseball  30% Depends also on surface, which can absorb some of the ball’s energy

Physics Spring 2012 Totally Inelastic Collisions

Physics Spring 2012 Totally Inelastic Collision

Physics Spring 2012 Inelastic Collisions Case 1: V g = + 1 m/s, V or = 0 m/s Case 2: V g = + 1 m/s, V or = - 4 m/s m = 5 kgm = 1 kg

Physics Spring 2012 Class Problem A 100 kg ogre clobbers a dainty 50 kg figure skater while trying to learn to ice-skate. If the ogre is moving at 6 m/s before the collision, and the skater is at rest, at what speed will the tangled pile be sliding afterwards? A) 0 m/s B) 3 m/s C) 4 m/s D) 5 m/s E) 6 m/s

Physics Spring 2012 More Complicated Collisions

Physics Spring 2012 Class problems 1) The difference between impulse and impact force involves the A) time the force acts. B) mass and its effect on resisting a change in momentum. C) difference between acceleration and velocity. D) distance the force acts. 2)It is correct to say that impulse is equal to A) the force multiplied by the distance the force acts. B) momentum. C) the change in momentum. D) velocity multiplied by time

Physics Spring 2012 Class Problems 3) A large heavy truck and a small baby carriage roll down a hill. Neglecting friction, at the bottom of the hill, the baby carriage will have a greater A) acceleration. B) speed. C) momentum. D) all of these E) none of these 4) Compared to falling on a stone floor, a wine glass may not break when it falls on a carpeted floor because the A) carpeted floor provides a smaller impulse. B) stopping time is shorter on the carpet. C) stopping time is longer on the carpet. D) carpet provides a smaller impulse and a longer time.

Physics Spring 2012 Class Problems 5) A 1-N apple falls to the ground. The apple hits the ground with an impact force of about A) 4 N. B) 9.8 N. C) 1 N. D) 2 N. E) not enough information given to say 6) An astronaut, floating alone in outer space, throws a baseball. If the ball floats away at a speed of 20 meters per second, the astronaut will A) move in the opposite direction, but at a lower speed. B) move in the opposite direction but at a higher speed. C) move in the opposite direction at a speed of 20 m/s. D) not move as stated in any of the above choices.